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Fox/Levin/Forde, Elementary Statistics in Social Research, 12e. Chapter 10: Correlation. HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 5/5/2014 , Spring 2014. Final Exam. Monday 5/19/2014 Time and Place of the class Chapters 9, 10 and 11

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Presentation Transcript
final exam
Final Exam
  • Monday 5/19/2014
  • Time and Place of the class
  • Chapters 9, 10 and 11
  • Same format as past two exams
  • No re-submission of homework
  • Summer SAS Course
differentiate between the strength and direction of a correlation
Learning Objectives
    • After this lecture, you should be able to complete the following Learning Outcomes
  • 10.1
Differentiate between the strengthand direction of a correlation
correlation
10.1Correlation

Until now, we’ve examined the presence or absence of a relationship between two or more variables

What about the strength and direction of this relationship?

  • We refer to this as the correlation between variables

Strength of Correlation

  • This can be visualized using a scatter plot
    • Strength increases as the points more closely form an imaginary diagonal line across the center

Direction of Correlation

  • Correlations can be described as either positive or negative
    • Positive – both variables move in the same direction
    • Negative – the variables move in opposite directions
slide5

10.1

Figure 10.1

slide6

10.1

Figure 10.2

identify a curvilinear correlation
Learning Objectives
    • After this lecture, you should be able to complete the following Learning Outcomes
  • 10.2
Identify a curvilinear correlation
curvilinear correlation
10.2Curvilinear Correlation

A relationship between X and Y that begins as positive and becomes negative, or begins as negative and becomes positive

discuss the characteristics of correlation coefficients
Learning Objectives
    • After this lecture, you should be able to complete the following Learning Outcomes
  • 10.3
Discuss the characteristics of correlation coefficients
the correlation coefficient
10.3The Correlation Coefficient

Numerically expresses both the direction and strength of a relationship between two variables

  • Ranges between -1.0 and + 1.0

Direction

  • Strength
  • The sign (either – or +) indicates the direction of the relationship
  • Values close to zero indicate little or no correlation
  • Values closer to -1 or +1, indicate stronger correlations
calculate and test the significance of pearson s correlation coefficient r
Learning Objectives
    • After this lecture, you should be able to complete the following Learning Outcomes
  • 10.4
Calculate and test the significance of Pearson’s correlation coefficient (r)
pearson s correlation coefficient r
10.4Pearson’s Correlation Coefficient (r)

Focuses on the product of the X and Y deviations from their respective means

  • Deviations Formula:
  • Computational Formula:
testing the significance of pearson s r
10.4Testing the Significance of Pearson’s r

The null hypothesis states that no correlation exists in the population (ρ = 0)

  • To test the significance of r, at ratio with degrees of freedom N – 2 must be calculated

A simplified method for testing the significance of r

  • Compare the calculated r to a critical value found in Table H in Appendix C
exercises
Exercises

Problem 6, 19, 21

requirements for the use of pearson s r correlation coefficient
10.4Requirements for the Use of Pearson’s r Correlation Coefficient
  • A Straight-Line Relationship
  • Interval Data
  • Random Sampling
  • Normally Distributed Characteristics
calculate the partial correlation coefficient
Learning Objectives
    • After this lecture, you should be able to complete the following Learning Outcomes
  • 10.5
Calculate the partial correlation coefficient
partial correlation
10.5Partial Correlation

The correlation between two variables, X and Y, after removing the common effects of a third variable, Z

When testing the significance of a partial correlation, a slightly different t formula is used

exercise
Exercise

Problem 30

homework
Homework

Problems 18, 22 and 31

Add interpretation

slide21

CHAPTER SUMMARY

  • Correlation allows researchers to determine the strength and direction of the relationship between two or more variables

10.1

  • In a curvilinear correlation, the relationship between two variables starts out positive and turns negative, or vice versa

10.2

  • The correlation coefficient numerically expresses the direction and strength of a linear relationship between two variables

10.3

  • Pearson’s correlation coefficient can be calculated for two interval-level variables

10.4

  • The partial correlation coefficient can be used to examine the relationship between two variables, after removing the common effect of a third variable

10.5